Analytical Analysis of The Dual-phase-lag Heat Transfer Equation in a Finite Slab with Periodic Surface Heat Flux (RESEARCH NOTE)

Abstract

This work uses the dual-phase-lag (DPL) model of heat conduction to demonstrate the effect of temperature gradient relaxation time on the result of non-Fourier hyperbolic conduction in a finite slab subjected to a periodic thermal disturbance. DPL model combines the wave features of hyperbolic conduction with a diffusion-like feature of the evidence not captured by the hyperbolic case. For the first time, the analytical solution of DPL model of heat conduction equation is obtained adopting Laplace transform method and inversion theorem. The temperature profiles at the front and rear surfaces of the slab are calculated for various temperature gradient relaxation time. The phase and amplitude difference between the front and the rear surface are calculated numerically as a function of the temperature gradient relaxation time, which are reported previously as a function of the heat flux relaxation time. The results demonstrate that increasing on the temperature gradient relaxation time leads to the lower phase difference and upper amplitude difference between the temperature responses of the front and rear surfaces.